Average Error: 0.0 → 0.0
Time: 9.2s
Precision: 64
Internal Precision: 128
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{e}^{\left((x \cdot x + -1)_*\right)}\]

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[e^{-\left(1 - x \cdot x\right)}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{e^{(x \cdot x + -1)_*}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.0

    \[\leadsto e^{\color{blue}{1 \cdot (x \cdot x + -1)_*}}\]

  5. Applied exp-prod0.0

    \[\leadsto \color{blue}{{\left(e^{1}\right)}^{\left((x \cdot x + -1)_*\right)}}\]

  6. Simplified0.0

    \[\leadsto {\color{blue}{e}}^{\left((x \cdot x + -1)_*\right)}\]

  7. Final simplification0.0

    \[\leadsto {e}^{\left((x \cdot x + -1)_*\right)}\]

Reproduce

herbie shell --seed 2019068 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))